The Economics of Money Banking and Financial Markets
The Economics of Money, Banking, and Financial Markets Twelfth Edition Chapter 4 The Meaning of Interest Rates Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Preview • Before we can go on with the study of money, banking, and financial markets, we must understand exactly what the phrase interest rates means. In this chapter, we see that a concept known as the yield to maturity is the most accurate measure of interest rate. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Learning Objectives • Calculate the present value of future cash flows and the yield to maturity on the four types of credit market instruments. • Recognize the distinctions among yield to maturity, current yield, rate of return, and rate of capital gain. • Interpret the distinction between real and nominal interest rates. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Measuring Interest Rates • Present value: a dollar paid to you one year from now is less valuable than a dollar paid to you today. – Why: a dollar deposited today can earn interest and become $1×(1+i) one year from today. – To understand the importance of this notion, consider the value of a $20 million lottery payout today versus a payment of $1 million per year for each of the next 20 years. Are these two values the same? Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Present Value Let i =. 10 In one year: $100 × (1 + 0. 10) = $110 In two years: $110 × (1 + 0. 10) = $121 or $100 × (1 + 0. 10)2 In three years: $121 × (1 + 0. 10) = $133 or $100 × (1 + 0. 10)3 In n years $100 × (1 + i)n Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Simple Present Value (1 of 2) PV = today’s (present) value CF = future cash flow (payment) i = the interest rate Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Simple Present Value (2 of 2) • Cannot directly compare payments scheduled in different points in the time line Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Four Types of Credit Market Instruments • Simple Loan • Fixed Payment Loan • Coupon Bond • Discount Bond Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Yield to Maturity • Yield to maturity: the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Yield to Maturity on a Simple Loan Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Fixed-Payment Loan The same cash flow payment every period throughout the life of the loan LV = loan value FP = fixed yearly payment n = number of years until maturity Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Coupon Bond (1 of 4) Using the same strategy used for the fixed-payment loan: P = price of coupon bond C = yearly coupon payment F = face value of the bond n = years to maturity date Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Coupon Bond (2 of 4) • When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate. • The price of a coupon bond and the yield to maturity are negatively related. • The yield to maturity is greater than the coupon rate when the bond price is below its face value. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Coupon Bond (3 of 4) Table 1 Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years (Face Value = $1, 000) Price of Bond ($) Yield to Maturity (%) 1, 200 7. 13 1, 100 8. 48 1, 000 10. 00 900 11. 75 800 13. 81 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Coupon Bond (4 of 4) • Consol or perpetuity: a bond with no maturity date that does not repay principal but pays fixed coupon payments forever P = C / ic Pc = price of the consol C = yearly interest payment Ic = yield to maturity of the consol can rewrite above equation as this: ic = C/Pc For coupon bonds, this equation gives the current yield, an easy to calculate approximation to the yield to maturity Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Discount Bond For any one year discount bond F = Face value of the discount bond P = Current price of the discount bond The yield to maturity equals the increase in price over the year divided by the initial price. As with a coupon bond, the yield to maturity is negatively related to the current bond price. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
The Distinction Between Interest Rates and Returns (1 of 4) • Rate of Return: Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
The Distinction Between Interest Rates and Returns (2 of 4) • The return equals the yield to maturity only if the holding period equals the time to maturity. • A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period. • The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interestrate change. • Interest rates do not always have to be positive as evidenced by recent experience in Japan and several European states. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
The Distinction Between Interest Rates and Returns (3 of 4) • The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate. • Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
The Distinction Between Interest Rates and Returns (4 of 4) Table 2 One-Year Returns on Different-Maturity 10%-Coupon. Rate Bonds When Interest Rates Rise from 10% to 20% (1) (2) Years to Maturity Initial When Bond Is Current Purchased Yield (%) (3) (4) (5) Initial Price Rate of Price Next Capital Gain ($) Year* ($) (%) (6) Rate of Return [col (2) + col (5)] (%) 30 10 1, 000 503 − 49. 7 − 39. 7 20 10 1, 000 516 − 48. 4 − 38. 4 10 10 1, 000 597 − 40. 3 − 30. 3 5 10 1, 000 741 − 25. 9 − 15. 9 2 10 1, 000 917 − 8. 3 +1. 7 1 10 1, 000 0. 0 +10. 0 *Calculated with a financial calculator, using Equation 3. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Maturity and the Volatility of Bond Returns: Interest-Rate Risk • Prices and returns for long-term bonds are more volatile than those for shorter-term bonds. • There is no interest-rate risk for any bond whose time to maturity matches the holding period. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
The Distinction Between Real and Nominal Interest Rates • Nominal interest rate makes no allowance for inflation. • Real interest rate is adjusted for changes in price level so it more accurately reflects the cost of borrowing. – Ex ante real interest rate is adjusted for expected changes in the price level – Ex post real interest rate is adjusted for actual changes in the price level Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Fisher Equation Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Figure 1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953– 2017 Sources: Nominal rates from Federal Reserve Bank of St. Louis FRED database: http: //research. stlouisfed. org/fred 2/. The real rate is constructed using the procedure outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investigation, ” Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151– 200. This procedure involves estimating expected inflation as a function of past interest rates, inflation, and time trends, and then subtracting the expected inflation measure from the nominal interest rate. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved.
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